Admissible Regions for Higher-Order Finite Volume Method Grids. Issue 2 (2nd May 2017)

• Record Type: Journal Article
• Authors: Zhang, Yuanyuan; Chen, Zhongying
• Is Part Of: East Asian journal on applied mathematics. Volume 7:Issue 2(2017)
• Page Start: 269
• Page End: 285
• Publication Date: 2017-05-02
• Subjects: 65N30, -- 65N12; Finite volume method, -- admissible region, -- uniform local-ellipticity; Applied mathematics -- Periodicals; 519.05
• DOI: 10.4208/eajam.290416.161016a
• Languages: English
• ISSNs: 2079-7362

Abstract

Abstract: Admissible regions for higher-order finite volume method (FVM) grids are considered. A new Hermite quintic FVM and a new hybrid quintic FVM are constructed to solve elliptic boundary value problems, and the corresponding admissible regions are investigated. A sufficient condition for the uniform local-ellipticity of the new hybrid quintic FVM is obtained when its admissible region is known. In addition, the admissible regions for a large number of higher-order FVMs are provided. For the same class of FVM (Lagrange, Hermite or hybrid), the higher order FVM has a smaller admissible region such that stronger geometric restrictions are required to guarantee its uniform local-ellipticity.